I grew up in Augusta, GA in the 50's and used to watch a local old time wooden barrel maker (cooper)build barrels. "Stavin' chain" is an old term for the steel chain used to temporarily clamp and hold loose barrel staves together in a circle, edge to edge, while a barrel is being built, so that the metal hoops can be driven over the staves to tighten them into a barrel. The chain is fairly heavy steel, and the metaphor is obvious, particularly considering the song's year of origin, when wooden barrels were still a major shipping container, and the cathouse locale. I'm surprised no one has come up with this so far!